Library works ok, tested on (clone) Uno and 16 x 2 display so great functionality wise. A little improvement though.

I find function naming conventions a bit too explicit though e.g

lcd.PCF8574_LCDResetScreen(HD44780LCD::LCDCursorTypeOff);

or

lcd.PCF8574_LCDSendString("Hello World!");

as I see lot of redundant PCF8574 and LCD words here. Could be simply

lcd.write("Hello World!");

or

lcd.reset(HD44780LCD::CursorOff);

as class HD44780LCD namespaces all within so there is no naming collisions with other writes or resets or anything else. Also calls such as

lcd.PCF8574_LCDGOTO(HD44780LCD::LCDLineNumberOne, 0);

could be written in more concise way

lcd.goto(0, 0); // goto first line, first column

as I don't see any value of enuming lines.

Anyway, thanks for the work, works perfect.

The function 'HD44780LCD::PCF8574_LCDGOTO' sets the cursor to the desired position by calculating bitwise OR of the line address and the column number. This works well with the starting values of line one (0x80) and line 2 (0xC0) as well as the 16col values for line 3 (0x90) and line 4 (0xD0).
But for 20 column LCD the starting values for line 3 (0x94) and line 4 (0xD4) do not work.
The base values are correct, but the bitwise OR lead to wrong position.
Please see red marked cells in image for reference.

I suggest using a simple addition the calculate the LCD ADDRESS.

for STM32 Connect SDA and SCL to B7 and B6 respectively (just saying as its not stated anywhere I could find). Worked a treat thanks even on CKS32!

Is it possible to add a way to set the I2C port to use on the Bluepill? It is done on the example I2C scanner so would be a nice addition.